#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
#define dbgv(v) cout<<#v<<" = "; f(i,0,int(v.size())) cout<<v[i]<<" "; cout<<endl
#define dbga(a,x,y) cout<<#a<<" = "; f(i,x,y) cout<<a[i]<<" "; cout<<endl
#define erorp(x) cout<<#x<<"={"<<x.F<<" , "<<x.S<<"}"<<endl
#define eror(x) cout<<#x<<'='<<(x)<<endl
#define f_(i,a,b) for(int i=a;i>=b;i--)
#define f(i,a,b) for(int i=a;i<b;i++)
#define nb(x) __builtin_popcount(x)
#define all(v) v.begin(),v.end()
#define bit(n,k) (((n)>>(k))&1)
#define Add(x,y) x=(x+y)%mod
#define maxm(a,b) a=max(a,b)
#define minm(a,b) a=min(a,b)
#define lst(x) x[x.size()-1]
#define sz(x) int(x.size())
#define mp make_pair
#define ll long long
#define pb push_back
#define S second
#define F first
const int N=1e5+99,mod=1e9+9;
int mark[N];
ll pow(ll x,ll y,ll mod){return(!y?1:pow(x*x%mod,y/2,mod)*(y&1?x:1))%mod;}
int valid(int n, int inputSeq[]){
f(i,0,n) inputSeq[i]--;
f(i,0,n) if(++mark[inputSeq[i]]>1) return 0;
f(i,0,n){
if(inputSeq[i]<n){
f(j,0,n){
if(inputSeq[(i+j)%n]!=(inputSeq[i]+j)%n && inputSeq[(i+j)%n]<n) return 0;
}
return 1;
}
}
return 1;
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[]){
vector<pair<int,int>> vec;
f(i,0,n) gondolaSeq[i]--;
int b=0,l=0;
f(i,0,n){
if(gondolaSeq[i]<n){
b=1;
f(j,0,n){
if(gondolaSeq[(i+j)%n]>=n){
vec.pb(mp(gondolaSeq[(i+j)%n],(gondolaSeq[i]+j)%n));
}
}
break ;
}
}
if(b==0){
f(i,0,n){
vec.pb({gondolaSeq[i],i});
}
}
sort(all(vec));
int prv=n-1;
for(auto p : vec){
replacementSeq[l++]=p.S;
f(i,prv+1,p.F) replacementSeq[l++]=i;
prv=p.F;
}
f(i,0,l) replacementSeq[i]++;
return l;
}
//----------------------
int countReplacement(int n, int inputSeq[])
{
vector<pair<int,int>> vec;
f(i,0,n) inputSeq[i]--,mark[inputSeq[i]]=0;
f(i,0,n) if(++mark[inputSeq[i]]>1) return 0;
int b=0;
f(i,0,n){
if(inputSeq[i]<n){
b=1;
f(j,0,n){
if(inputSeq[(i+j)%n]!=(inputSeq[i]+j)%n && inputSeq[(i+j)%n]<n){
return 0;
}
if(inputSeq[(i+j)%n]>=n){
vec.pb(mp(inputSeq[(i+j)%n],(inputSeq[i]+j)%n));
}
}
break ;
}
}
if(b==0){
f(i,0,n){
vec.pb({inputSeq[i],i});
}
}
sort(all(vec));
int prv=n-1,ans=1;
f(i,0,vec.size()){
pair<int,int> p=vec[i];
int cnt=vec.size()-i;
//cout<<cnt<<" -> "<<p.F-prv<<endl;
ans=1ll*ans*pow(cnt,p.F-prv-1,mod)%mod;
prv=p.F;
}
return ans;
}
